x=(6x-3)(7x-7)

Solution for x=(6x-3)(7x-7) equation:

Simplifying
x = (6x + -3)(7x + -7)

Reorder the terms:
x = (-3 + 6x)(7x + -7)

Reorder the terms:
x = (-3 + 6x)(-7 + 7x)

Multiply (-3 + 6x) * (-7 + 7x)
x = (-3(-7 + 7x) + 6x * (-7 + 7x))
x = ((-7 * -3 + 7x * -3) + 6x * (-7 + 7x))
x = ((21 + -21x) + 6x * (-7 + 7x))
x = (21 + -21x + (-7 * 6x + 7x * 6x))
x = (21 + -21x + (-42x + 42x2))

Combine like terms: -21x + -42x = -63x
x = (21 + -63x + 42x2)

Solving
x = 21 + -63x + 42x2

Solving for variable 'x'.

Reorder the terms:
-21 + x + 63x + -42x2 = 21 + -63x + 42x2 + -21 + 63x + -42x2

Combine like terms: x + 63x = 64x
-21 + 64x + -42x2 = 21 + -63x + 42x2 + -21 + 63x + -42x2

Reorder the terms:
-21 + 64x + -42x2 = 21 + -21 + -63x + 63x + 42x2 + -42x2

Combine like terms: 21 + -21 = 0
-21 + 64x + -42x2 = 0 + -63x + 63x + 42x2 + -42x2
-21 + 64x + -42x2 = -63x + 63x + 42x2 + -42x2

Combine like terms: -63x + 63x = 0
-21 + 64x + -42x2 = 0 + 42x2 + -42x2
-21 + 64x + -42x2 = 42x2 + -42x2

Combine like terms: 42x2 + -42x2 = 0
-21 + 64x + -42x2 = 0

Begin completing the square.  Divide all terms by
-42 the coefficient of the squared term: 

Divide each side by '-42'.
0.5 + -1.523809524x + x2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + -1.523809524x + -0.5 + x2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + -1.523809524x + x2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + -1.523809524x + x2 = 0 + -0.5
-1.523809524x + x2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
-1.523809524x + x2 = -0.5

The x term is -1.523809524x.  Take half its coefficient (-0.761904762).
Square it (0.5804988664) and add it to both sides.

Add '0.5804988664' to each side of the equation.
-1.523809524x + 0.5804988664 + x2 = -0.5 + 0.5804988664

Reorder the terms:
0.5804988664 + -1.523809524x + x2 = -0.5 + 0.5804988664

Combine like terms: -0.5 + 0.5804988664 = 0.0804988664
0.5804988664 + -1.523809524x + x2 = 0.0804988664

Factor a perfect square on the left side:
(x + -0.761904762)(x + -0.761904762) = 0.0804988664

Calculate the square root of the right side: 0.283723221

Break this problem into two subproblems by setting 
(x + -0.761904762) equal to 0.283723221 and -0.283723221.

Subproblem 1
x + -0.761904762 = 0.283723221

Simplifying
x + -0.761904762 = 0.283723221

Reorder the terms:
-0.761904762 + x = 0.283723221

Solving
-0.761904762 + x = 0.283723221

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.761904762' to each side of the equation.
-0.761904762 + 0.761904762 + x = 0.283723221 + 0.761904762

Combine like terms: -0.761904762 + 0.761904762 = 0.000000000
0.000000000 + x = 0.283723221 + 0.761904762
x = 0.283723221 + 0.761904762

Combine like terms: 0.283723221 + 0.761904762 = 1.045627983
x = 1.045627983

Simplifying
x = 1.045627983

Subproblem 2
x + -0.761904762 = -0.283723221

Simplifying
x + -0.761904762 = -0.283723221

Reorder the terms:
-0.761904762 + x = -0.283723221

Solving
-0.761904762 + x = -0.283723221

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.761904762' to each side of the equation.
-0.761904762 + 0.761904762 + x = -0.283723221 + 0.761904762

Combine like terms: -0.761904762 + 0.761904762 = 0.000000000
0.000000000 + x = -0.283723221 + 0.761904762
x = -0.283723221 + 0.761904762

Combine like terms: -0.283723221 + 0.761904762 = 0.478181541
x = 0.478181541

Simplifying
x = 0.478181541

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.045627983, 0.478181541}